January 2014, Vol. 45, Issue 1
Obstacles and Affordances for Integer Reasoning: An Analysis of Children’s Thinking and the History of Mathematics
Jessica Pierson Bishop, Lisa L. Lamb, Randolph A. Philipp, Ian Whitacre, Bonnie P. Schappelle, and Melinda L. Lewis
The authors identify and document 3 cognitive obstacles, 3 cognitive affordances, and 1 type of integer understanding that can function as either an obstacle or affordance for learners while they extend their numeric domains from whole numbers to include negative integers. In particular, the authors highlight 2 key subsets of integer reasoning: understanding or knowledge that may, initially, interfere with one’s learning integers (which they call cognitive obstacles) and understanding or knowledge that may afford progress in understanding and operating with integers (which they call cognitive affordances).
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